Histograms

Histograms

Question 1
Medium46%

The table shows information about the age of 80 teachers.

Age (years)Frequency
20<a≤3020 < a \leq 3020<a≤3020
30<a≤3530 < a \leq 3530<a≤3522
35<a≤4035 < a \leq 4035<a≤4016
40<a≤5040 < a \leq 5040<a≤5013
50<a≤6550 < a \leq 6550<a≤659

On the grid, draw a histogram for the information in the table.

A blank grid for drawing a histogram.

[3]
Question 2
Medium

The table shows information about the mass, in grams, of some parcels.

Mass (m m\,m g)Frequency
0<m≤200 < m \leq 200<m≤2010
20<m≤3020 < m \leq 3020<m≤3015
30<m≤3530 < m \leq 3530<m≤3514
35<m≤4035 < m \leq 4035<m≤40
40<m≤6040 < m \leq 6040<m≤608
a.

Use the information on the table to complete the histogram.

A histogram grid for the mass of parcels.

[2]
b.

Use the histogram to complete the table.

[2]
Question 3
Medium

The histogram shows information about the mass of several parcels in a delivery van.

A histogram showing the distribution of parcel masses. Frequency densities are: 0-10kg: 2.0; 10-15kg: 3.0; 15-25kg: 3.0; 25-30kg: 2.0; 30-50kg: 1.0.

a.

Work out an estimate for the proportion of parcels with a mass over 27.5kg.

[3]
b.

Explain why your answer to part a is only an estimate.

[1]
Question 4
Medium

The table shows information about the height, in cm, of some plants in a greenhouse.

Height (h h\,h cm)Frequency
0<h≤100 < h \leq 100<h≤1015
10<h≤1510 < h \leq 1510<h≤1525
15<h≤2015 < h \leq 2015<h≤2020
20<h≤3020 < h \leq 3020<h≤30
30<h≤5030 < h \leq 5030<h≤5010
a.

Use the information in the table to complete the histogram.

A histogram on a grid showing plant heights.

[2]
b.

Use the histogram to complete the table.

[2]
Question 5
Medium

The table shows information about the time, in minutes, taken by 71 students to complete a puzzle.

Time (t t\,t minutes)Frequency
0<t≤100 < t \leq 100<t≤1012
10<t≤1510 < t \leq 1510<t≤1515
15<t≤2515 < t \leq 2515<t≤2520
25<t≤3025 < t \leq 3025<t≤3014
30<t≤5030 < t \leq 5030<t≤5010

On the grid, draw a histogram for the information in the table.

A blank grid for drawing a histogram.

[3]
Question 6
Medium

The table shows information about the masses, in kg, of some packages.

Mass (m m\,m kg)Frequency
0<m≤100 < m \leq 100<m≤1010
10<m≤1510 < m \leq 1510<m≤1515
15<m≤2515 < m \leq 2515<m≤2540
25<m≤3025 < m \leq 3025<m≤3015
30<m≤5030 < m \leq 5030<m≤5010
a.

On the grid, draw a histogram for the information in the table.

A blank grid for drawing a histogram.

[3]
b.

Work out an estimate for the number of packages with a mass over 28 kg.

[1]
Question 7
Medium

The table shows information about the height of 90 young trees.

Height (h h\,h cm)Frequency
0<h≤100 < h \leq 100<h≤1015
10<h≤1510 < h \leq 1510<h≤1520
15<h≤2515 < h \leq 2515<h≤2540
25<h≤4025 < h \leq 4025<h≤4015
a.

On the grid, draw a histogram for the information in the table.

A blank grid for drawing a histogram.

[3]
b.

Find an estimate for the median.

[2]
Question 8
Medium

The histogram shows information about the speed of cars passing a checkpoint.

A histogram showing Frequency Density on the y-axis and Speed (mph) on the x-axis.

40 cars have a speed between 40 and 50 mph.

a.

Work out an estimate for the number of cars which have a speed of more than 65 mph.

[3]
b.

Explain why your answer to part a is only an estimate.

[1]
Question 9
Medium

The table shows information about the speed, in mph, of some cars.

Speed (mph)Frequency
40<s≤5540 < s \leq 5540<s≤556
55<s≤6055 < s \leq 6055<s≤6010
60<s≤6560 < s \leq 6560<s≤6546
65<s≤7565 < s \leq 7565<s≤7548
75<s≤9075 < s \leq 9075<s≤906
a.

On the grid, draw a histogram for the information in the table.

A blank grid for drawing a histogram.

[3]
b.

Work out an estimate for the number of cars over 70mph.

[1]
Question 10
Medium

The histogram shows information about the time taken by members of a running club to complete a 10km race.

A histogram showing race completion times. Frequency densities are: 0-20 mins: 0.5; 20-30 mins: 1.2; 30-40 mins: 1.8; 40-60 mins: 0.7; 60-90 mins: 0.2.

a.

Work out an estimate for the proportion of runners who took longer than 50 minutes.

[3]
b.

Explain why your answer to part a is only an estimate.

[1]
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Histograms Questions

Practise AQA GCSE Maths Histograms with exam-style questions for Foundation and Higher tier. 28 questions, matched to the AQA GCSE Maths (8300) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Histograms Questions

  1. GCSE
  2. /Maths
  3. /Histograms